Let X ~ Geom(p), let n be a non-negative integer, and let Y ~ Bin(n, p). Show that P(X = n) = (l/n)(1/n)p(Y=1).
Step 1 of 1:
Where mean and variance .
Here non-negative integer is n.
Our goal is :
We need to prove that P(X=n)=.
Now we have to prove that P(X=n)=.
The formula of the geometric distribution is
Where q = (1-p)
The formula of the binomial distribution is
Here the probability of X is n and the probability of Y is 1.
Here and = p.